A389909 a(n) = 2*A064989(n) for odd n, a(n) = A003961(n/2) for even n, where A003961 is fully multiplicative with a(p) = nextprime(p), and A064989 is its left inverse.

2, 1, 4, 3, 6, 5, 10, 9, 8, 7, 14, 15, 22, 11, 12, 27, 26, 25, 34, 21, 20, 13, 38, 45, 18, 17, 16, 33, 46, 35, 58, 81, 28, 19, 30, 75, 62, 23, 44, 63, 74, 55, 82, 39, 24, 29, 86, 135, 50, 49, 52, 51, 94, 125, 42, 99, 68, 31, 106, 105, 118, 37, 40, 243, 66, 65, 122, 57, 76, 77, 134, 225, 142, 41, 36, 69, 70, 85, 146

Offset

1,1

Comments

Self-inverse permutation (involution) of natural numbers.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to prime indices in the factorization of n.

Index entries for sequences that are permutations of the natural numbers.

Formula

For all n >= 1, A252463(n) = A252463(a(n)).

Prog

(PARI)
A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A064989(n) = { my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f) };
A389909(n) = if(n%2, 2*A064989(n), A003961(n/2));

Crossrefs

Interleaving of A243502 and A003961.

Cf. A064989, A252463, A389910.

Sequence in context: A306230 A382375 A071065 * A359946 A328654 A035552

Adjacent sequences: A389906 A389907 A389908 * A389910 A389911 A389912

Keyword

nonn,easy

Author

Antti Karttunen, Nov 16 2025

Status

approved